Final answer:
The equation of line BC is 7x + 5y = 24.
Step-by-step explanation:
To find the equation of line BC, we need to find the slope of line BC and a point on that line. Since AC and BC form a right angle at point B, the slope of BC is the negative reciprocal of the slope of AC. The slope of AC can be found using the formula (change in y)/(change in x):
Slope of AC = (y2-y1)/(x2-x1) = (4 - (-1))/(4 - (-3)) = 5/7
Therefore, the slope of BC is -7/5. Since point B is on line BC, we can substitute the values of x and y for B into the equation y = mx + b, where m is the slope and b is the y-intercept, to solve for b:
4 = (-7/5)(4) + b
b = 24/5
So the equation of line BC is y = -7/5x + 24/5. Convert this equation to standard form by multiplying through by 5:
5y = -7x + 24
7x + 5y = 24